# Capital Asset Pricing Model (CAPM)

In this article, Jayati WALIA (ESSEC Business School, Grande Ecole – Master in Management, 2019-2022) presents Capital Asset Pricing Model(or CAPM).

## Introduction

The Capital Asset Pricing Model (CAPM) is a widely used metrics for the financial analysis of the performance of stocks. It shows the relationship between the expected return and the systematic risk of investing in an asset. The idea behind the model is that the higher the risk in an investment in securities, the higher the returns an investor should expect on his/her investments.

The Capital Asset Pricing Model was developed by financial economists William Sharpe, John Lintner, Jack Treynor and Jan Mossin independently in the 1960s. The CAPM is essentially built on the concepts of the Modern Portfolio Theory (MPT), especially the mean-variance analysis model by Harry Markowitz (1952).

CAPM is very often used in the finance industry to calculate the cost of equity or expected returns from a security which is essentially the discount rate. It is an important tool to compute the Weighted Average Cost of Capital (WACC). The discount rate is then used to ascertain the Present Value (PV) and Net Present Value (NPV) of any business or financial investment.

## CAPM formula

The formula for capital asset pricing model takes into consideration different components to compute the expected return of a security.

E(R)= R_{f} + β(E(R_{m} )- R_{f})

With the following notations:

E(R): Expected return of the stock

R_{f}: Risk-free interest rate

β: Beta of the stock

E(R_{m}): Expected return of the market

The risk premium for the market is equal to E(R_{m} )- R_{f} and the risk premium for the stock is equal to β(E(R_{m} )- R_{f}).

The formula shows that investors demand a return higher than the risk-free rate for taking higher risk. The equity risk premium is the component that reflects the excess return investors require on their investment which is multiplied by the beta.

Let us discuss the components of the Capital Asset Pricing Model individually:

### Expected return of the security: E(R)

The expected return of the security is essentially the minimum return that the investor should demand when investing his/her money in the security. It can also be considered as the discount rate the investor can utilize to ascertain the value of the security.

### Risk-free interest rate: R_{f}

The risk-free interest rate is usually taken as the yield on debt issued by the government (the 3-month Treasury bills and the 10-year Treasury bonds in the US) as they are the safest investments. As government bonds have very rare chances of default, their interest rates are considered risk-free.

### Beta: β

The beta is a measure of the systematic or the non-diversifiable risk in a stock. This essentially means the sensitivity of a stock price compared to the overall market. The market beta is equal to 1. A beta greater than 1 for a stock signifies that the stock is riskier compared to the overall market, and a beta of less than 1 signifies that the stock is less risky compared to the overall market.

The beta is calculated by using the equation:

With the following notations:

R: return of the stock

R_{m}: return of the market

The beta of a stock is defined as the ratio of the covariance between the stock return and the market return, and the variance of the market return.

The covariance is a measure of correlation between two random variables. In practice, the covariance is calculated using historical data for the stock return and the market return.

The variance is a measure of the dispersion of returns. The standard deviation, equal to the square root of the variance, is a measure of the volatility in the market returns over time.

### Expected market returns

The expected market return is usually computed using historical data of the market. The market is usually represented by a stock index to which the stock belongs to.

For example, for calculating the expected return on APPLE stock, we usually consider the S&P 500 index. Historically, the expected return for the S&P 500 index is around 9%.

## Assumptions in Capital Asset Pricing Model

The CAPM considers the following assumptions which forms the basis for the model:

- Investors are risk averse and rational – In the CAPM, all investors are assumed to be risk averse. They diversify their portfolio which neutralizes the non-systematic or the diversifiable risk. So, in the end only the systematic or the market risk is considered to calculate the expected returns on the security.
- Efficient markets – The markets are assumed to be efficient, thus all investors have equal access to the same information. Also, all the assets are considered to be liquid, and an individual investor cannot influence the future prices of an asset.
- No transaction costs – The CAPM assumes that there are no transaction costs, taxes, and restrictions on borrowing or lending activities.
- Risk premium – The CAPM model assumes that investors require higher premium for more risk they take (risk aversion).

## Example

As an example, lest us consider an investor who wants to calculate the expected return on an investment in APPLE stock. Let’s see how the CAPM can be used in this case.

The risk-free interest rate is taken to be the current yield on 10-year US Treasury bonds. Let us assume that its value is 3%.

The S&P 500 index has an expected return of 9%.

The beta on APPLE stock is 1.25.

The expected return on APPLE stock is equal to 3% + 1.25*(9% – 3%) = 10.50%

## Useful resources

### Acadedmic articles

Lintner, J. (1965) The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets *The Review of Economics and Statistics* 47(1) 13-37.

Markowitz, H. (1952) Portfolio Selection *The Journal of Finance* 7(1) 77-91.

Mossin, J. (1966) Equilibrium in a Capital Asset Market *Econometrica* 34(4) 768-783.

Merton, R.C. (1973) An Intertemporal Capital Asset Pricing Model *Econometrica* 41(5) 867-887.

Sharpe, W.F. (1964) Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk *The Journal of Finance* 19(3) 425-442.

### Business sources

Corporate Finance Institute CAPM

Mullins, D.W. Jr (1982) Does the Capital Asset Pricing Model Work? Harvard Business Review.

## Related posts on the SimTrade blog

▶ Walia J. Linear Regression

▶ Beta

## About the author

The article was written in September 2021 by Jayati WALIA (ESSEC Business School, Grande Ecole – Master in Management, 2019-2022).